Let's be clear about a few things:
"No budget" is a euphemism for "we think photographers are mugs". This offensive interpretation can easily be verifed by trying the phrase at your local restaurant, eg "I have no budget for dinner but I'd like to eat". Adding a promise to tell all your friends where you ate will not deflect your head from the kerb as the manager throws you out.
Now imagine being a restaurant where most people who come through the door try this on. The answer is NO, and I am being excessively polite.
If you didn't really mean it and your "no budget" claim was just an opening bid, the answer is still NO. I want nothing to do with greedy opportunists who try to commence a negotiation with a lie. You have already demonstrated you cannot be trusted. You probably won't be honest about usage, and will try not to pay.
And if you were one of those promising lots of better, paid work later, if only I can help you out now, offer a contract else I'll know you're talking bullshit and the answer is of course NO.
You see I don't want your "free exposure", I want mutually beneficial, productive relationships with clients. I try to behave with integrity, honesty and fairness, and I expect clients will do likewise. Exposure is the end of that process, not a means. Similarly with bylines. I don't require applause earned by being a sucker. If free matters more than good, ask someone else.
Like most people I work because I need to pay bills and support myself, my work and my family. The fact that I love what I do is why I have spent 40 years persevering whilst going without stuff most people take for granted. Vocation is not an invitation to disrespect.
Some people do not understand that my photos only exist because I have invested time and money and learning in creating them.
Unsurprisingly I will not support questionable business models that rely on exploiting photography, or me, to extinction. With very rare exceptions (small charities run by unpaid volunteers that I choose to support) I have no budget for subsidising other peoples' work and profitability. Supporting my own is next to impossible thanks to the current vogue for passing off exploitation as opportunity.
When I can afford it, I will drop a few quid into a charity box or give to a homeless person on the street. I regularly work for charities at a discounted rate. I look after baby birds that have fallen out of nests. I am a generous, kind and loving human being. But I make an exception for salaried beggars who ask me to stuff a bundle of tenners in their pocket. They just piss me off. Especially when they insult me by telling me my life's work is jolly nice but worthless.
Supply without payment is, of course, only viable for hobbyist photographers who don't need an income from their photography. They have salaried jobs, pensions or private incomes, or perhaps suicidal romantic tendencies. I do not. They have a selfish attitude to destroying the sustainability of photography as a profession which they call "beating the pro's at their own game". Moreover a byline might appeal to their idiot vanity. I suggest you ask one of them. Alternatively find a new graduate or student to exploit - they are desperate and naive, and you have the opportunity to add to their crippling student debt by saving yourself a few quid.
If all this means you can't source the images you want, that is just tough. I can't source free cameras, computers, software, food, housing, fuel, either. If it's all so damn easy and cheap, go and make your own photos.
If all this offends you, best stay away from mirrors too.